Coffee Filter Drag
The purpose of this laboratory investigation is to observe and determine the effect of air on a falling object. To do this, you will drop a coffee filter (or stack of filters) and measure the downward motion. In Part A you will simply use a stopwatch to time filters falling a set distance for several trials. In Part B you will do a single trial measuring a falling stack of filters using a motion detector.
The experimental result will be compared to theories for air resistance in which the drag is assumed to be either proportional to speed or speed squared. The air resistance acting on the filter should most closely follow the equation F = k2v2. However, a reasonable model can often be achieved with F = k1v. In either case, the constant k in the equation is related to the density of the air, the cross-sectional area of the object, and the degree to which the object has an aerodynamic shape. The values of the two constants will be different for a given object.
In this part of the experiment you will measure the relationship between drag and speed for an object of a given size and shape. In the experiment that follows you will vary only the mass of the falling object without significantly changing its cross-sectional area or shape.
1. Take a stack of seven coffee filters (do not separate the filters). Drop the stack of filters from a set height and measure the time for the filters to fall this distance. Record the distance and time in the data table.
2. Remove a single filter from the stack and label it with the number seven. Then repeat the experiment with a stack of six coffee filters. Record the time.
3. Remove another filter and label it with the number six and repeat the experiment with a stack of five coffee filters. Continue like this until you have completed the time column of data.
4. Use an electronic balance to determine the total mass of each stack that fell in each trial.
In this part of the experiment you will produce a single velocity graph of a falling stack of coffee filters by collecting data with a Go Direct Motion detector. Use a stack of only two filters. Record the mass of the stack used for Part B.
Collecting Data Using Motion Detector
1. Connect the Go Direct Motion detector to Graphical Analysis running on a laptop (either by cable or Bluetooth). Measure the motion of a stack of two filters falling through the air. The motion detector may be placed on the floor below the falling stack of two filters. Or, the it may be held stationary above the falling stack. Either way, the goal is to get a smooth record of the velocity of the falling stack – starting from rest and approaching terminal velocity (it is okay if it does not reach terminal velocity).
2. Inspect the velocity vs. time graph. There often will be large erroneous spikes on the graph that make it hard to view the valid data that is actually of interest. It is important to “zoom in” on the part of the velocity graph that actually shows only the falling of the stack of filters (and does not show impact with the floor or any other event). In order to zoom in, click and drag to select an interval of time and then click the button to Zoom to Selection.
3. A word about dropping the filter: it is important that your moving hands do not affect the motion of the filter. For example, if you pull your hand downward out from under the filter it will tend to get dragged down by the draft created by your hand. The best technique is to hold the filter with both hands – one on either side – and then move your hands horizontally outward and away from the filter. This will minimize disturbance of the air directly below the filter.
4. Repeat the experiment as many times as necessary to get one satisfactory set of data for a single drop of the stack of two filters. Feel free to adjust data collection parameters such as duration of the experiment (the default of 5 seconds is more than needed), and rate (default is 20 per second).
5. Once a satisfactory set of data has been obtained go to the File menu and Save the file. Share the file of motion detector data with each member of your group by whatever means you find most convenient.
1. Complete the data table for part A by computing weight, speed, speed squared, and the values of the “constants” k1 and k2. Enter units for each constant. The constants are found by assuming that the speed measured is the terminal speed (in which case there is no acceleration). Determine the best values (i.e. mean) for each constant.
2. Using your determinations of weight and terminal speed produce a graph of drag vs. speed. (Weight and drag are balanced when falling at terminal speed!) Use a calculator or computer to determine the best fit using a “power regression” of type y = A xB . Plot the curve produced by the equation so that it may be compared to the data. Include the equation on the graph.
3. Produce a graph of drag vs. speed squared. Use a calculator or computer to determine the best fit using a linear regression. Plot the line produced by the equation so that it may be compared to the data. Include the equation and correlation coefficient on the graph.
4. Adjust the settings in Graphical Analysis to produce a single graph showing Velocity vs. Time, focusing only on the interval of time during which the filter stack was falling freely through the air. Include enough data to show the actual point where the stack was released – i.e. changed from being held at rest to falling through the air.
5. Apply an exponential curve fit to the data points that best show the motion through air. Make any appropriate adjustments to the appearance of the graph to finalize it and maximize its effectiveness for the lab report. Default settings are not always best!
6. Use appropriate tools to save the graph in a form that may be printed. This would include taking a screenshot or using the Export feature in the file menu of Graphical Analysis.
1.
Consider the exponential curve fit on the velocity vs. time graph. Use
the equation and its coefficients (as determined by the computer’s regression)
to answer the following. Show work and/or explain each response.
(a) Determine the terminal speed indicated by the equation.
(b) Determine a value of k1 based on the equation and the mass
of the filter.
(c) Determine the initial acceleration of the filter just as it was dropped.
2.
The model F = kv2 is more specifically written
as F = ½ CDAρ
v2, where A = cross-sectional area, ρ = density of air, and CD
= the coefficient of drag – a dimensionless quantity that characterizes the
aerodynamic shape of the body. The more aerodynamic and streamlined the body,
the closer the coefficient of drag is to zero. Use your value of k2
to determine the coefficient of drag for a coffee filter. Show your work
clearly.
(density of air ρ = 1.2 kg/m3)
3. Based on the tables, graphs, etc. which model – speed or speed squared – do you feel most accurately models air resistance acting on a falling coffee filter? Be specific and support your position.
4. Quantify percent error and/or percent deviation by at least one calculation. Show your work and clearly label (error in what, deviation in what).
5. Discuss error. What are signs of error in the results, tables, graphs, etc? How about the results of the calculations in question #1? What are the most likely sources of the error that is apparent?
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Outer diameter of filters = |
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Drag model: F = k1v |
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Drag model: F = k2v2 |
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Distance fallen by filters = |
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m (g) |
wt. (N) |
time (s) |
speed (m/s) |
k1 ( ) |
speed2 (m2/s2) |
k2 ( ) |
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7 |
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6 |
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5 |
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4 |
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2 |
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1 |
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mean k1 = |
mean k2 = |
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Part B – Velocity vs. Time
Mass of two-filter stack: _________________
A complete report (50 pts) consists of the following items arranged in this order: